2.1 what are numbers. the rational numbers

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2.1 Wha Ae Nmbe? The Raional Nmbe

W natural numbers, 1, 2, 3, .

I , 20 ( ), . W ,

, , , , , .

I , .

What operations?

T addition, subtraction, multiplication division ( uglification derision according to

Lewis Carroll who was a well known mathematician).

Y add , ,

.

S, , . I , 5, , , . W 0 zero. A

, 5, , 3, , ,

-2, "minus two".

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. Z ,

.

N , . S

, 11 . T , -6,

,

. S , 5

, .

S , " " ,

0 . T ,

, 0 integers, Z.

W Z Z.

I know all that, but I am very rusty on actual additions and subtractions. I get them wrong much of the time I

try to do them.

M .

T , 1234123 5432121

.

F . Y

, . U I

, . A

I , . T

, .


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I . T

. H .

W "summands" . I

, ( )

,

.

A, , . F ,

431 512 1 2 1.

I , , ,

.

T 5 , undoes 5 . T,

, , , : 3 + 5 - 5

= 3.

A 5 5 inverse , : Performing

them one after the other is equivalent to doing nothing.

B multiplication. T

product. Y (I )

.

I was never ver good at this.

I , ,

.

N ,

+ - * = .

(Unfortunatel this fact has led pedagogues to believe the do not have to force pupils to go through the drudger of

learning the multiplication table.

This does much harm to those who don't bother to do so, because of the wa our brains function. It turns out that the

more time we spend on an activit as children, and even as adults, the bigger the area of the brain gets that is devoted

to that activit, and the bigger it gets, the better we get at that activit.

Thus, our spending less time learning the multiplication table has the effect of reducing the area of our brain

devoted to calculation, which impedes our further mathematical development.

Your skill at mathematics will be directl proportional to the amount of time ou choose to devote to thinking about it.And that is up to ou.)

O , : ? W

, 5, ? T

division. S .

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we want to be able to define division wherever we can.

Ratios of integers are called rational numbers, and ou get one for an pairs of integers, so long as the second integer,

called the denominator, is not ero. Ratios like which are not themselves integers are called fractions.

Once we have introduced fractions, we want to provide rules for adding and subtracting them and for multipling and

dividing them. These start to get complicated, but fortunatel for us, we have calculators and spreadsheets that can do

these things without complaining at all if we have the wit to enter what we want done.

There is one thing we cannot do with our rational numbers, and that is to divide b 0. Division, after all, is the action of

undoing multiplication. But multipling an number b 0 gives result 0. There is no wa to get back from this 0

product what ou multiplied 0 b to get it.

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2.1 what are numbers. the rational numbers

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